During Lunar New Year, Jason, a dedicated mobile gamer, is addicted to playing "Kingdom Defence". To win the game, he needs to maximize his total power to defeat the final boss. The game involves arranging $N$ troops, where the $i$-th troop has power of $i$, in some order and construct a permutation $P$. A permutation is a sequence of integers from $1$ to $N$ of length $N$ containing each number exactly once. Mathematically, the total score is calculated by $$\sum_{i=1}^{N-K+1} \left(\max_{j=i}^{i+K-1} P_j\right)$$ In other words, you are asked to arrange the numbers from $1$ to $N$ in a way that maximizes the sum of the maximum value in each contiguous subarrays of size $K$. You, an expert of the game, are asked to help him to create the best permutation $P$ of the numbers $1$ to $N$ that maximizes the total power.

Input

The only line of the input contains two integers, $N$ and $K$.

Output

Output the best permutation $P$ in a single line.
If there are multiple answers, you can output any of them.

Constraints

For all cases, $1 \le K \le N \le 10^5$
Subtask 1 (20%): $1 \le K \le N \le 10$
Subtask 2 (25%): $1 \le K \le N \le 20$
Subtask 3 (25%): $1 \le K \le N \le 10^3, 0 \le N - K \le 10$
Subtask 4 (30%): No additional constraints